The equation of the tangent to the curve `y=4xe^(x)` at `(-1,(-4)/e)` is

Options

A. `y=-1`
B. `y=-(4)/(e)`
C. `x=-1`
D. ` x=(-4)/(e)`

Answer

B

Explanation

Given curve is `y=4xe^(x)`
`(dy)/(dx)=4e^(x)+4xe^(x)`
At `(-1,-(4)/(e))((dy)/(dx))_((-1,-4//e))=4e^(-1)+4(-1)e^(-1)=0`
`:.` Equation of tangent is
`(y+(4)/(e))=0(x+1)`
`implies y=-(4)/(e)`